Question

Given that z is a standard normal random variable, compute the following probabilities.

a. P(0 < < 0.61)
b. P(-1.60 c. P(Z > 0.46)
d. P(Z > -0.44)
e. P(z < 2.01)
f. P(Z <-0.72)

Answer 1

To compute the given probabilities, use the standard normal distribution table or a calculator with a standard normal distribution function. The standard normal distribution has a mean of 0 and a standard deviation of 1.

Step-by-step explanation:

To compute the given probabilities, we need to use the standard normal distribution table or a calculator with a standard normal distribution function. The standard normal distribution has a mean of 0 and a standard deviation of 1. Here are the calculations for each probability:

a. P(0 < z < 0.61) = P(z < 0.61) - P(z < 0) = 0.7257 - 0.5 = 0.2257

b. P(-1.60 < z < 0) = P(z < 0) - P(z < -1.60) = 0.5 - 0.0548 = 0.4452

c. P(z > 0.46) = 1 - P(z < 0.46) = 1 - 0.6772 = 0.3228

d. P(z > -0.44) = 1 - P(z < -0.44) = 1 - 0.3306 = 0.6694

e. P(z < 2.01) = P(z < 2.01) = 0.9778

f. P(z < -0.72) = P(z < -0.72) = 0.2357